Displaying similar documents to “Symmetries and currents in nonholonomic mechanics”

Conservation laws and symmetry in economic growth models: a geometrical approach.

Manuel de León, David Martín de Diego (1998)

Extracta Mathematicae

Similarity:

The aim of the present paper is twofold. On one hand, we present a classification of infinitesimal symmetries for Lagrangian systems, and the corresponding Noether theorems. The derivation of the result is made by using the symplectic techniques. Some of the results were previously obtained by other authors (see Prince (1985) for instance), and an exhaustive presentation can be found in de León and Martín de Diego (1995, 1996). Let us note that these results are true even if the Lagrangian...

Solving non-holonomic Lagrangian dynamics in terms of almost product structures.

Manuel de León, David Martín de Diego (1996)

Extracta Mathematicae

Similarity:

Given a Lagrangian system with non-holonomic constraints we construct an almost product structure on the tangent bundle of the configuration manifold such that the projection of the Euler-Lagrange vector field gives the dynamics of the system. In a degenerate case, we develop a constraint algorithm which determines a final constraint submanifold where a completely consistent dynamics of the initial system exists.

Geometric mechanics on nonholonomic submanifolds

Olga Krupková (2010)

Communications in Mathematics

Similarity:

In this survey article, nonholonomic mechanics is presented as a part of geometric mechanics. We follow a geometric setting where the constraint manifold is a submanifold in a jet bundle, and a nonholonomic system is modelled as an exterior differential system on the constraint manifold. The approach admits to apply coordinate independent methods, and is not limited to Lagrangian systems under linear constraints. The new methods apply to general (possibly nonconservative) mechanical...